Obama tours a factory in Asheville, North Carolina, on Wednesday after making his pitch for a higher minimum wage. Photograph: Brendan Smialowski/AFP/Getty Images

Business groups and Republicans rounded on Barack Obama on Wednesday over one of the most contentious elements of his state of the union speech: his proposal to increase the minimum wage.

The president set out plans to increase the federal minimum wage from $7.25 an hour to $9 in his address to Congress on Tuesday night. "Tonight, let's declare that in the wealthiest nation on earth, no one who works full-time should have to live in poverty, and raise the federal minimum wage to $9 an hour," said Obama.

He claimed the move would raise incomes for "millions of working families" and would benefit businesses by putting more money in the pockets of consumers.

Obama pushed for the rise again Wednesday while touring a manufacturing plant in Asheville, North Carolina. "If you work full-time, you shouldn't be in poverty," Obama said.

But business leaders and Republicans rallied against the proposal. Business Roundtable president John Engler said: "We should be focused on our country's 'no wage' problem. We need an economic growth agenda to get our economy going and put Americans back to work."

Matthew Shay, the National Retail Federation president and chief executive officer, said: "Before we debate the federal minimum wage, we need a broad, comprehensive plan from Washington that encourages businesses to plan, invest and grow this economy. So far, all we have are interim steps and uncertainty, none of which inspire confidence or create an environment that leads to economic growth, investment and job security."

They were backed by Republican House speaker John Boehner. "When you raise the price of employment, guess what happens? You get less of it," Boehner said. "What happens when you take away the first couple of rungs on the economic ladder, you make it harder for people to get on the ladder. Our goal is to get people on the ladder, and help them climb that ladder so they can live the American dream."

Obama's proposal would raise the minimum wage in several stages. After that, there would be an annual increase in the minimum wage pegged to inflation. "In fact, working folks shouldn't have to wait year after year for the minimum wage to go up while CEO pay has never been higher," said Obama.

The president suggested upping the minimum wage to $9.25 by 2011 when he first ran for president in 2008. The White House argues that 15m people would see their wages rise as a result.

Nineteen states already have minimums that exceed the current federal level. The higher level, whether federal or local, takes precedent. One state, Washington, already exceeds Obama's proposal at $9.19 an hour. Some companies, including Costco, the retail discount chain, have come out in support of an increase.

Michael Cannon, director of health policy studies at the Cato Institute, a libertarian thinktank, said the move would be counterproductive. "President Obama is knocking out another few rungs on the economic ladder, guaranteeing that more people will not be able to climb it."

He said the proposal would hurt rather than help those on low wages, pushing low skilled workers out. "In a competitive market, business will not pay people more than their productivity justifies," he said.